A137710 Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); left border = (1, 2, 4, 8, 16, 32, ...).

1, 2, 1, 4, 1, 1, 8, 2, 1, 1, 16, 4, 2, 1, 1, 32, 8, 3, 2, 1, 1, 64, 16, 6, 2, 2, 1, 1, 64, 16, 6, 2, 2, 1, 1, 128, 32, 12, 5, 2, 2, 1, 1, 256, 64, 24, 10, 4, 2, 2, 1, 1, 512, 128, 48, 21, 9, 4, 2, 2, 1, 1, 1024, 256, 96, 42, 19, 18, 4, 2, 2, 1, 1, 2048, 512, 192, 84, 40, 18, 18, 4, 2, 2, 1, 1

Offset

1,2

Comments

Row sums = A137711: (1, 3, 6, 12, 24, 47, 92, 183, ...).

Eigensequence of the triangle = even-indexed Fibonacci numbers starting (1, 3, 8, 21, 55, ...). Cf. triangle A180339. - Gary W. Adamson, Aug 28 2010

Links

Table of n, a(n) for n=1..85.

Formula

The triangle is generated by two rules: T(n,k) = T(n-1, k-1) - T(n-k, k-1); and left border = 1, 2, 4, 8, 16, ...

Example

First few rows of the triangle:
    1;
    2,   1;
    4,   1,  1;
    8,   2,  1,  1;
   16,   4,  2,  1, 1;
   32,   8,  3,  2, 1, 1;
   64,  16,  6,  2, 2, 1, 1;
  128,  32, 12,  5, 2, 2, 1, 1;
  256,  64, 24, 10, 4, 2, 2, 1, 1;
  512, 128, 48, 21, 9, 4, 2, 2, 1, 1;
  ...

Crossrefs

Cf. A137711.

Cf. A180339. - Gary W. Adamson, Aug 28 2010

Sequence in context: A283826 A088443 A117352 * A068009 A140168 A059119

Adjacent sequences: A137707 A137708 A137709 * A137711 A137712 A137713

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 08 2008

Status

approved